Gray, Alison and Greenhalgh, David and Mao, Xuerong and Pan, Jiafeng
(2012)
*SDE SIS epidemic models.*
In: Workshop on Stochastic Modelling in Ecosystems, 2012-06-11 - 2012-06-12, Glasgow.
(Unpublished)

## Abstract

In this paper we extend the classical susceptible-infected-susceptible epidemic model from a deterministic framework to a stochastic one and formulate it as a stochastic differential equation (SDE) for the number of infectious individuals $I(t)$. We then prove that this SDE has a unique global positive solution $I(t)$ and establish conditions for extinction and persistence of $I(t)$. We discuss perturbation by stochastic noise. In the case of persistence we show the existence of a stationary distribution and derive expressions for its mean and variance. The results are illustrated by computer simulations, including two examples based on real-life diseases.

Item type: | Conference or Workshop Item (Speech) |
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ID code: | 41322 |

Keywords: | Susceptible-infected-susceptible model, pneumococcus, gonorrhea, stationary distribution, basic reproduction number, persistence, extinction, stochastic differential equations, Brownian motion, Probabilities. Mathematical statistics |

Subjects: | Science > Mathematics > Probabilities. Mathematical statistics |

Department: | Faculty of Science > Mathematics and Statistics |

Depositing user: | Pure Administrator |

Date Deposited: | 02 Oct 2012 10:05 |

Last modified: | 11 Dec 2015 06:34 |

URI: | http://strathprints.strath.ac.uk/id/eprint/41322 |

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